Probabilistic age classification with Bayesian networks: A study on the ossification status of the medial clavicular epiphysis
Introduction
Since knowing the age of an individual is necessary for a large number of social and juridical situations (both civil and criminal), the practice of age estimation of living persons has extremely gained in importance in the past few decades [1], [2], [3], [4]. This is mostly due to the increase in cross-border migration movements or human trafficking involving people unable to provide valid documentary evidence for attesting their age [5]. Generally, the range of ages having a particular legal interest is between 14 and 22 years of age, thus it is essential to be able to estimate the chronological age across this interval and/or to decide whether an individual belongs to a given age class included in this range [3], [4]. According to some approaches, such as those proposed by the Study Group on Forensic Age Diagnostic (AGFAD) and the Forensic Anthropology Society of Europe (FASE) [6], age estimation should be appropriately based on the examination of some physical attributes, generally related to bones and dental maturation [4], [7], [8]. The age estimation is usually performed in two steps: first, the degree of maturity reached by a physical indicator is assessed in ordered developmental stages or through the assignment of score values [9], [10], [11]. Then, the observed degree of maturity is converted into the estimated chronological age or in the probability that the individual is included in a meaningful range of ages by means of different statistical methods, usually related to a specific physical attribute. Results should be provided in an appropriate form in order to fulfill the specific forensic and legal needs. From this point of view, the Bayesian approach is particularly suited because it allows the user to coherently deal with the uncertainty related to age estimation and to provide results in a transparent and logical form [12]. Some Bayesian methods allow one to update an initial (or prior) belief about the chronological age of the examined individual in the light of the observed degree of maturity of a given physical attribute [12], [13], [14]. Results are then provided in the form of a posterior probability distribution, which encapsulates all uncertainty associated with the estimated quantity, i.e., the chronological age. This distribution is then used to compute the probability that the examined individual is younger or older than an age threshold of interest, such as the age of majority [12], [13], [14]. The practical application of Bayesian methods can be facilitated to a great extent by using specific probabilistic graphical tools, such as Bayesian networks [15]. Bayesian networks combine elements of both graph and probability theories. The first one is applied to qualitatively define the structure of the model, taking into account the variables of interest (represented by nodes) and their respective probabilistic relationships (represented by directed arcs). The probability theory is then applied to define the nature of these relationships and to quantify their strength [15], [16]. Recently, a Bayesian network for age estimation was presented in scientific literature [14]. The network allows users to take into account evidence related to the degree of maturity observed in an examined individual and to provide both posterior probability distribution on the chronological age, as well as the posterior probabilities that the individual is older or younger than a given age threshold.
The aim of this paper is to study the performances of the Bayesian network in classifying individuals as younger or older than 18 years of age (i.e., the age of majority in numerous countries worldwide) on the basis of data related to the medial clavicular epiphysis development. Therefore, misclassifications (i.e., the rate of false minors and false majors) were investigated. Furthermore, the influence of prior probabilities assignment was also inspected. Analyses were performed using a sample available in scientific literature [17]. Note that the sample cannot serve as reference database and it was used only for exploratory analysis.
Section snippets
Material
For the analysis exposed in this paper, the data sample presented by Kreitner et al. was used [17]. The sample contains 380 European white subjects (males and females) under the age of 30 years lacking of development disorders. Each subject is described by his or her age and the classification of the degree of maturity reached by the medial clavicular epiphysis. The degree of maturity was assessed by an experienced radiologist according to a traditional four-stage classification [17], [18] by
Methods
Analyses were carried out with the Bayesian network for age estimation [14]. The structure of the network considers three variables: the chronological age (node Age in Fig. 1), the degree of maturity reached by the medial clavicular epiphysis, expressed in form of the assigned developmental stage (node Stage in Fig. 1) and the event that the examined individual is younger or older than 18 years of age. This latter is expressed in the form of two mutually exclusive propositions, P1: the examined
Performances in classification
Fig. 3 shows the distribution of the ORPost obtained with the model (e.g. Bayesian network). Descriptive statistics of these distributions are shown in Table 3.
The model well discriminates the two propositions of interest avoiding in that way the existence of ambiguous evaluative situations. This is shown in the histograms of Fig. 3, where all distributions of ORPost, given a particular stage, take a specific range of value with no overlapping. This means that the ORPost always corroborates one
Discussion
A sample related to the ossification status of the medial collar bone epiphysis was used for a preliminary investigation of the efficiency of the Bayesian network proposed in [14] for dealing with the classification of individuals (older or younger than 18 years of age). The development of the clavicle can be described by a few stages [18], [27], [28], making this physical attribute more suitable for a probabilistic classification of individuals according to a given age threshold rather than
Conclusion
In this paper, the performance of a probabilistic Bayesian method was tested in classifying young individuals as majors or minors based on their ossification status observed in the medial clavicular epiphysis. The Bayesian method was applied by means of the Bayesian network presented in [14]. Due to the nature of the data sample employed for the analyses, these latter are only explorative, however, the results obtained are promising, considering the low rate of misclassification encountered.
Acknowledgements
The authors wish to thank Ph.D. Cyril Muehlethaler for the proofreading. They are also grateful to the anonymous reviewers for their valuable comments.
References (31)
- et al.
Aging the dead and the living
Forensic age estimation
- et al.
The problem of aging human remains and living individuals: a review
Forensic Sci. Int.
(2009) - et al.
Bayesian networks
- et al.
Reliability of the methods applied to assess age minority in living subjects around 18 years old. A survey on a Moroccan origin population
Forensic Sci. Int.
(2005) - et al.
An introduction to the history of age estimation in the living
Advances in forensic age estimation
Forensic Sci. Med. Pathol.
(2012)- et al.
Immigration, asylum seekers and undocumented identity
- et al.
Criteria for age estimation in living individuals
Int. J. Legal Med.
(2008) - et al.
Key practical elements for age estimation in the living
Practical imaging techniques for age evaluation
Age evaluation and odontology in the living
Age evaluation from the skeleton
The presentation of results and statistics for legal purposes
Human dental age estimation using third molar developmental stages: does a Bayesian approach outperform regression models to discriminate between juveniles and adults?
Int. J. Legal Med.
Cited by (11)
A collection of idioms for modeling activity level evaluations in forensic science
2023, Forensic Science International: SynergyAn evaluation of statistical models for age estimation and the assessment of the 18-year threshold using conventional pelvic radiographs
2020, Forensic Science InternationalCitation Excerpt :Linear regression models were also used for age estimation [6,19], which were inappropriate for ordinal variables [20,21]. Some researchers have applied more sophisticated variable selection techniques, such as support vector machine (SVM) [22], decision tree [23], logistic regression [23], transition analysis [24] and Bayesian networks [25], to estimate age with better accuracy. However, few models have been tested on the pelvis.
Age estimation of living persons: A coherent approach to inference and decision
2020, Statistics and Probability in Forensic AnthropologyBayesian networks of age estimation and classification based on dental evidence: A study on the third molar mineralization
2018, Journal of Forensic and Legal MedicineCitation Excerpt :This result can be achieved thanks to the intuitive nature of the CPTs linked to each node in the networks that allow users to entry and modify conditional and unconditional probabilities in an easy and intuitive way. For instance, the likelihood function for the evaluation of evidence form a single tooth was assessed in the present study by applying an unrestricted cumulative probit model to the reference sample, but other ordinal regression models have already been employed for age estimation,19,45 even in Bayesian networks13,43; ease the concrete computations in the inferential framework, since the probabilistic tool automatically provides the outcomes of interest avoiding the user to have to deal with the computational complexity of the algebraic handling of Bayes' theorem;
Ink dating part II: Interpretation of results in a legal perspective
2018, Science and JusticeCitation Excerpt :Until now, such a model has never been tested for ink dating using real reference data, only subjective probabilities were used to show the potential of this interpretation approach [2,19,30]. Different models were proposed in the literature, including Baysenets, for different ageing problematics such as evaluating the time since discharge [23], the moment of deposition of fingermarks [24], or the age of living people [25,26]. Each model has to take into account specificities such as the type of hypotheses (e.g. punctual times versus intervals), the type of data (e.g. continuous or discreet, uni or multivariate) and the type of ageing processes (e.g. regression fits and factors influencing transfer and influence storage).
Towards a Bayesian evaluation of features in questioned handwritten signatures
2017, Science and JusticeCitation Excerpt :As a consequence, information I is usually omitted from explicit graphical representation in Bayesian networks. Bayesian networks are very flexible, and have been used to support evaluative reasoning in very different forensic branches such as firearms [5], printed documents [6], signatures [7], forensic medicine [8] and DNA [9]. A review on the usage of Bayesian networks in forensic science can be found in Ref. [10].